Everybody and their dog is getting a 4K screen soon. What I've run across are both true 4K movies, and movies that say they are 4K.
I have found that true 4K movies have tremendous extra detail. You can watch the movie again and again, and see different things when focussing on one corner or another. In 4K, I like slow, scenic movies. Action/thriller movies do not improve with 4K because your eye is always drawn to the main action.
Only a very small spot on the screen can be resolved by the eye while watching.
Then we have 'not really 4K' movies. These are modern movies that generate special effects that are cheaper by only doing lesser resolution. The special effects are 'murky' or mucked up by rain and darkness. You can't watch the corners. Worst, are the old films that they have pimped up to be called 4K. These were filmed with 35 mm film which is a max of 1080p. They use computer upscaling, which merely does what your brain does -- filling in standard details. There is no extra enjoyment in watching.
Just looked at a bit of LOTR '4K' release. It is nice and bright, and is good for first-time watchers, but doesn't add anything. The special effects are mucky. I only watched 10 minutes.